Colorfulom has given great directions, since you are still hesitant, draw it out or even use a piece of paper to be the pieces and try it with the paper first. When I'm stuck on how to lay out backing I always draw it out first to check my measurements.
Your 10 yd of fabric should allow you to have a back that is 112 by 112" (assuming your usable width of fabric is 40").
This should give you enough extra for quilting on the DSM or handquilting. Depending on your LA quilter and the density of quilting planned, you may be little "short" on the LA, but still doable.